Math 2.0

Proposition

Counting lemma

Statement

The counting lemmas this article discusses are statements in combinatorics and graph theory. The first one extracts information from ϵ\epsilon-regular pairs of subsets of vertices in a graph GG, in order to guarantee patterns in the entire graph; more explicitly, these patterns correspond to the count of copies of a certain graph HH in GG. The second counting lemma provides a similar yet more general notion on the space of graphons, in which a scalar of the cut distance between two graphs is correlated to the homomorphism density between them and HH.

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first. The path takes the proof Proof of Counting lemma.

Show the path as a graph
Proof of Counting lemma, proof, no evidence levelProof of Counting lem…proofCounting lemma, statement, no evidence levelCounting lemmastatement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Proof of Counting lemma proof
  2. Counting lemma statement

Further reading

  1. Wikipedia, page 62471938, revision 1315423087, Counting lemma. adopted
About this page
TagWXB05RHWTY
URIm2://WXB05RHWTY
Kindstatement, proposition
WritingW0 stub
StatusThis copy of the site has no build data. Run m2 status WXB05RHWTY.
Same as
Changed4 November 2026

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What this page needs for W1

  • edge uses out: each definition that the statement needs (0 of 1)

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What links here

Proofs